In 1979, Zoeller became the first golfer since 1935 to win The Masters in his first appearance in the event. The only two other golfers to have won The Masters on their debut at Augusta were the winners of the first two Masters tournaments Horton Smith and Gene Sarazen, in 1934 and 1935 respectively. It was the first sudden-death playoff at The Masters; the previous six playoffs were 18-hole rounds on Monday (except 1935, which was 36 holes).

For much of his career, Zoeller was famous for waving a white towel in mock surrender from the fairway of the 72nd hole of the 1984 U.S. Open, after Greg Norman holed a long putt on the 72nd green to tie Zoeller for the tournament lead. At the end of the 18-hole playoff the next day between Norman and Zoeller (which Zoeller won by 8 strokes), Norman waved a white towel himself, returning the joke.

Zoeller was voted the 1985 winner of the Bob Jones Award, the highest honor given by the United States Golf Association in recognition of distinguished sportsmanship in golf.

Zoeller shared the 54-hole lead in the 1994 Open Championship after a 3rd round of 64, but finished the tournament in 3rd place, his best-ever finish in the British Open. Zoeller missed an 8-foot birdie putt on the 18th green in his 3rd round at Turnberry which would have tied the record for the best single round at the British Open.[2]

He competed at the 1979, 1983 and 1985 Ryder Cups, collecting 1.5 points in 10 matches.

Zoeller is often jokingly critical of his colleagues on the golf course, for instance, asking "Where are the windmills and animals?" on a newly designed golf course, or heckling Craig Stadler, saying, "Nice clods, Stadler. Did you get those at a Buster Brownfire sale?"[3]

At the 1997 Masters Tournament, Zoeller made what some considered to be a racist remark regarding Tiger Woods. After finishing tied for 34th place with a score of 78, Zoeller, referring to the following year's Masters Champions Dinner, for which the defending champion selects the menu, said, "He's doing quite well, pretty impressive. That little boy is driving well and he's putting well. He's doing everything it takes to win. So, you know what you guys do when he gets in here? You pat him on the back and say congratulations and enjoy it and tell him not to serve fried chicken next year. Got it." Zoeller then smiled, snapped his fingers, and walked away before turning and adding, "or collard greens or whatever the hell they serve."[4]K-Mart and Dunlop ceased sponsoring Zoeller after the incident.[5][6]

"I know Fuzzy, and it was obvious to me that he was attempting to be funny," fellow golf professional Tom Lehman said. "He probably would have said the same thing to Tiger's face and they both would have yukked it up...[But] it wasn't the best timing, and it wasn't in good taste. It's not appropriate."[4]

"I've been on the tour for 23 years and anybody who knows me knows that I am a jokester," Zoeller said. "It's too bad that something I said in jest was turned into something it's not. But I didn't mean anything by it and I'm sorry if I offend anybody. If Tiger is offended by it, I apologize to him, too. I have nothing but the utmost respect for Tiger as a person and an athlete."[7]

Zoeller later offered an apology directly to Woods, which Woods accepted.[8]

On February 13, 2007, Zoeller sued Josef Silny & Associates, a foreign-credential evaluation firm based in Miami, Florida. The lawsuit alleged that defamatory statements appeared in the Wikipedia article about Zoeller in December 2006, originating from a computer at that firm.[9][10] According to the suit, the edits suggested Zoeller had committed acts including alcohol, drugs and domestic abuse.[11] Defendant Josef Silny said a computer consultant would investigate.[12][13] However, Zoeller dropped the lawsuit in December 2007 after being unsuccessful in finding the poster.[14] Zoeller was unable to sue Wikipedia for the statements due to protections accorded to providers of "interactive computer services" under Section 230 of the Communications Decency Act.[15]